Explanation Given Information: The turbulent flow velocity data μ ( y ) , for air at 75 ˚ F and 1 atm near a smooth flat wall were taken in the University of Rhode Island wind tunnel: Concept Used: The density of air at that temperature and the kinematic viscosity of air at that temperature is calculated first by the method of interpolation. The equation of logarithmic overlap layer is stated as below: u u ∗ = 1 k ln y u ∗ v + B Here,u is the turbulent flow velocity, u ∗ is the friction velocity, y is the wall thickness, and k, B are the constants. The wall shear stress is calculated using the following: r w = ρ ( u ∗ a v g ) 2 Calculation: The density of air at temperature 75°F: 75 − 68 122 − 68 = ρ − ( 2.34 × 10 − 3 ) ( 2.12 × 10 − 3 ) − ( 2.34 × 10 − 3 ) ρ = 2.31 × 10 − 3 s l u g / f t 3 The kinematic viscosity of air at temperature 75°F: 75 − 68 122 − 68 = v − ( 1.61 × 10 − 4 ) ( 1.93 × 10 − 4 ) − ( 1.61 × 10 − 4 ) v = 1.65 × 10 − 4 f t 2 / s On substitution of 0.41 for k,5 for B and 1.65×10-4 ft 2 /s for v in the equation of logarithmic overlap layer. u u ∗ = 1 k ln y u ∗ v + B = 21 < To determine (b) To estimate: the velocity u at y = 0.22in.

8th Edition

ISBN: 9789385965494

Author: Frank White

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Question

Chapter 6, Problem 6.36P

To determine

(a)

To estimate: the wall shear stress.

To determine

(b)

To estimate: the velocity u at y = 0.22in.

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Chapter 6, Problem 6.35P

Chapter 6, Problem 6.37P

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